Question: Simplify to lowest terms. $\dfrac{45}{54}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 45 and 54? $45 = 3\cdot3\cdot5$ $54 = 2\cdot3\cdot3\cdot3$ $\mbox{GCD}(45, 54) = 3\cdot3 = 9$ $\dfrac{45}{54} = \dfrac{5 \cdot 9}{ 6\cdot 9}$ $\hphantom{\dfrac{45}{54}} = \dfrac{5}{6} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{45}{54}} = \dfrac{5}{6} \cdot 1$ $\hphantom{\dfrac{45}{54}} = \dfrac{5}{6}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{45}{54}= \dfrac{3\cdot15}{3\cdot18}= \dfrac{3\cdot 3\cdot5}{3\cdot 3\cdot6}= \dfrac{5}{6}$